Grays Athletic 0 York City 4: Brodie and City back on the goal trail
Midfielders Paul Harsley and Neil Barrett were also on target against a Grays team now without a win in 18 matches.
The result strengthened York's play-off claims ahead of a free Saturday this weekend.
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Hide AdGrays caused the visitors early problems with Jamie Guy hitting the crossbar and visiting defender Djoumin Sangare making a terrific goalline clearance after a poor punch from Michael Ingham.
On-loan Chesterfield player Harsley, though, broke the deadlock on 31 minutes for York, finding the bottom left-hand corner of Glyn Garner's net from eight yards.
Leading York marksman Brodie then scored his first goal since mid-January to double the visitors' advantage on 38 minutes.
The England C international cut inside home defender John Glowacki before firing home.
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Hide AdThree minutes later, Brodie netted his second of the night, pouncing from close range after Harsley's free-kick from the left.
York added their fourth on 57 minutes when Barrett fired past Garner from 12 yards.
Ingham was forced into making fine saves from Daniel Bunce and Alex Osborn as Julian Dicks's men refused to surrender despite the large deficit but the Essex club failed to grab a consolation goal.
Grays Athletic: Garner, Davis, Glowacki, Reynolds, Bunce, Cissoko (Harvey, 82), Dean, Graham (Wilson, 64), Agombar, Guy, Bayowa (Osborn, 70). Unused substitutes: Edwards, Clarey.
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Hide AdYork City: Ingham, Purkiss, Sangare (McGurk, 45), Graham, Meredith, Harsley, Clarke (Lawless, 64), Barrett, Pitt, Gash, Brodie (Rankine, 75). Unused substitutes: Smith, Carruthers.
Referee: J Adcock (Long Eaton).